How cerebellar architecture facilitates rapid online learning

The cerebellum has a distinctive circuit architecture comprising the majority of neurons in the brain. Marr-Albus theory and more recent extensions demonstrate the utility of this architecture for particular types of learning tasks related to the separation of input patterns. However, it is unclear how the circuit architecture facilitates known functional roles of the cerebellum. In particular, the cerebellum is critically involved in refining motor plans even during the ongoing execution of the associated movement. Why would a cerebellar-like circuit architecture be effective at this type of 'online' learning problem? We build a mathematical theory, reinforced with computer simulations, that captures some of the particular difficulties associated with online learning tasks. For instance, synaptic plasticity responsible for learning during a movement only has access to a narrow time window of recent movement errors, whereas it ideally depends upon the entire trajectory of errors, from the movement's start to its finish. The theory then demonstrates how the distinctive input expansion in the cerebellum, where mossy fibre signals are recoded in a much larger number of granule cells, mitigates the impact of such difficulties. As such, the energy cost of this large, seemingly redundantly connected circuit might be an inevitable cost of precise, fast, motor learning. ### Competing Interest Statement The authors have declared no competing interest.